Unlike the European states, Indian states are do not have a long running political history or national "myth". They have been formed based on linguistic similarity and for ease of administration. And they are not homogeneous either, hence there are multiple movements in place for further fragmentation (most of which are justified).

Also these states (or ancient / medieval kingdoms in them) have rarely been "at war" with each other. Until recently, India was sparsely populated and it was easy the "migrate" to another land to establish your kingdom rather than fight with your brother or cousin.

If you are interested, Francis Fukuyama [1] has a very interesting theory that says that India has been held together by its society and not its state. Multiple waves of invasion have not fundamentally altered the texture of the society, parts of the new culture have been slowly assimilated in it, often forcing the invaders to adapt to their new home.

[1] https://en.wikipedia.org/wiki/The_Origins_of_Political_Order